CN117148571A - Design method of infrared short wave band achromatic super lens and super lens - Google Patents
Design method of infrared short wave band achromatic super lens and super lens Download PDFInfo
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Abstract
The invention particularly relates to a design method of an infrared short wave band achromatic super lens and the super lens, the designed achromatic super lens is composed of a plurality of substructures, and the substructures are cylindrical silicon material nanorods taking glass as a substrate. Different from the common achromatic superlens, the invention designs a layer of Si3N4 film between the substrate and the nano rod based on the transmission phase regulation principle, and the film provides a part of phase compensation required by achromatism, so that the designed superlens realizes the achromatism function and reduces the influence of the phase compensation on the focusing effect so as to improve the focusing capability; finally, the super lens designed by the design method of the achromatic super lens of the infrared short wave band has good achromatic capability on the infrared short wave band of 1.3um to 1.7um, and simultaneously has very good focusing performance, and the focusing efficiency of any incident wave within the wavelength range of 1.3um to 1.7um is always kept above 0.75.
Description
Technical Field
The invention relates to the technical field of superlenses, in particular to a design method of an infrared short wave band achromatic superlens and the superlens.
Background
The superlens is also called superstructure lens, is a two-dimensional plane lens structure and is made of optical elements for focusing light on the supersurface. The super-lens is characterized by thinner volume, lighter weight, lower cost, better imaging and easier integration compared with the traditional lens, and can regulate and control the phase, amplitude and polarization of the light beam by virtue of the sub-wavelength structure. Superlenses offer a potential solution to compact integrated optical systems at the moment when conventional devices become increasingly bulky, high profile, relatively heavy, and are currently being studied in the optical field.
The core function of the superlens is realized by relying on phase modulation, and several methods of phase modulation are as follows: transmission-type phase modulation, geometric-type phase modulation, and resonance-type phase modulation. The most widely used of these is geometric phase modulation, where the target effect of the overall lens is achieved by a combination of designed micro-structured arrays. Transmission phase modulation is a technique of achieving phase modulation by allowing light to propagate through a predetermined dielectric layer, and theoretically has very good characteristics, but it is extremely dependent on the material properties and has difficulty in manufacturing, so that it is not commonly used because of its excessively low degree of freedom.
Due to the ultra-thin planar structure and the sub-structural unit size of the sub-wavelength level, and the combination of the design process and theory under the premise of high precision, the superlens generates serious chromatic aberration along with the wavelength change of the light wave, and how to eliminate chromatic aberration becomes an extremely important problem to be considered in the design of the superlens.
One widely used achromatism is to calculate the sum of the total phase differences due to the phase changes caused by the wavelength changes over a given band, introducing a constant that minimizes the number of this sum, i.e. to make:minimum, wherein: />Ideal phase formula for planar focusing superlens, +.>The phase profile for the designed superlens surface should be a function that is related to r only.
In the achromatic mode, the change of the surface phase distribution can deviate from an ideal phase formula, so that the focusing effect of the superlens is reduced, the focusing efficiency is reduced, the focusing light spot is enlarged, the use is not affected within a certain range, but the design of the superlens is still limited, and the allowable achromatic range of the superlens designed by the thought is smaller under the premise of ensuring the high focusing effect.
In view of the above, the present invention provides a method for overcoming the above technical problems.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a design method of an infrared short wave band achromatic superlens. The design method is based on the combination of transmission phase modulation and geometric phase modulation, so that the achromatic mode in the background technology is improved, the focusing efficiency of the achromatic superlens is improved, and the achromatic range of the superlens is widened.
The technical scheme adopted by the invention for solving the technical problems is as follows:
the design method of the achromatic superlens in the infrared short wave band comprises the following steps:
s1, determining a target achromatic wave band according to requirementsThe radius R of the super lens is used for determining the arrangement cycle number of a substructure forming the super lens and the cycle T of the substructure, wherein the center point of the substructure is positioned at the position which is away from the center mT of the lens, m is a natural number, the value range is [0, R/T ], and the substructure is a cylindrical nano rod made of silicon and takes glass as a substrate;
s2, according to the following surface phase distribution formulaPhase difference sum formula corresponding to each substructure +.>Performing comprehensive calculation to calculate the value of achromatic coefficient C corresponding to each substructure at each position so as to obtain the total phase difference formula +.>Taking the minimum value, and recording the corresponding relation between C and r at the moment, wherein f is the focal length of the superlens，λ 0 Is the midpoint of the wavelength range, r is the distance from the center point of the substructure to the center point of the superlens;
s3, according to the result of the achromatic coefficient C obtained in the step S2, the achromatic coefficient C is matched with a film transmission phase formulaSetting the film material and film thickness required by coating on the base, so thatTake the minimum value, will ∈>As a new achromatic coefficient, the surface phase formula required for the substructure is obtained>Wherein n is the refractive index of the film material, d is the thickness of the film, k is an integer value which is introduced by considering the superlens manufacturing difficulty factor, and the value range is [0,3]；
S4, modeling and parameter scanning are carried out on the substructure, proper heights are selected, the corresponding relation between the radius of the substructure and the corresponding surface phase distribution is obtained, and the corresponding relation is recorded in a phase library;
s5, calculating due surface phase data of each substructure according to the surface phase formula obtained in the step S3, and searching a radius value corresponding to the surface phase data in a phase library obtained in the step S4, so that the radius of each substructure at each position is determined, and modeling is carried out on each substructure according to the radius of each substructure at each position to obtain the modeling of the complete superlens.
Further, the calculation process in step S2 uses a particle swarm algorithm.
Further, the parameters of the scanning process in the step S4 are the high and the radius of the substructure, and the calculation of the scanning process is realized by a time domain finite difference method.
Further, the film layer provides a portion of the phase compensation required for achromatism using transmission phase modulation principles.
Further, the method comprises the following steps:
and S6, when the lens performance obtained by simulation cannot meet the requirement, returning to the step S1, resetting structural parameters of the unit substructure, including resetting the period, the film thickness, the material and the like, or returning to the step S3, and expanding the parameter scanning range.
Further, the infrared short wave band achromatic superlens designed according to the design method of the infrared short wave band achromatic superlens has a radius of 20um, a focal length of 90um and a numerical aperture of 0.217, and is composed of a substrate and a unit substructure arranged on the substrate according to rules, wherein the substrate material of the substructure is SiO 2 On which Si with a thickness of 0.101um is plated 3 N 4 The film, the base of substructure and each other combine the base that forms whole superlens, substructure cycle is 0.3um, the main part is cylindrical micro-nano structure, the cylinder material is silicon, cylinder height is 1um, radius is by spatial position and phase distribution determination, whole lens is not more than 2% in the infrared short wave band of 1.3um-1.7um by the focus skew that the colour difference leads to, and focusing efficiency is above 0.75, and the manufacturing degree of difficulty is basically the same with ordinary superlens.
Further, the radius of each unit substructure of the superlens is different, but is between 0.05um and 0.2 um.
Further, the array of sub-unit structures is arranged in a circular shape, and the number of the sub-structures on one radius is 67.
The invention has the following beneficial effects: compared with the prior art, the method reduces the influence of phase compensation on the focusing effect while realizing the achromatic function of the superlens, so that the achromatic range of the achromatic superlens is widened by phase change. Meanwhile, the manufacturing difficulty of the superlens is not increased, and a good idea is provided for the design of the achromatic superlens in the future.
Drawings
FIG. 1 is an overall top view of a superlens according to the present invention.
Fig. 2 is a partial image of a focal position of a general superlens as a function of light wavelength.
Fig. 3 is a partial image of the focal position of an achromatic superlens as a function of light wavelength.
Fig. 4 is a comparative image of the focusing efficiency of an achromatic superlens designed for two methods.
Detailed Description
In order to make the above features and advantages of the present invention more comprehensible, embodiments accompanied with figures are described in detail below. These examples are only for the purpose of illustrating the invention and are not intended to limit the scope of the invention in any way.
The invention relates to a design method of an infrared short wave band achromatic superlens, which comprises the following specific steps:
s1, determining a target achromatic wave band according to requirementsThe radius R of the super lens is used for determining the arrangement cycle number of a substructure forming the super lens and the cycle T of the substructure, wherein the center point of the substructure is positioned at the position which is away from the center mT of the lens, m is a natural number, the value range is [0, R/T ], and the substructure is a cylindrical nano rod made of silicon and takes glass as a substrate;
s2, according to the following surface phase distribution formulaPhase difference sum formula corresponding to each substructure +.>Performing comprehensive calculation to calculate the value of achromatic coefficient C corresponding to each substructure at each position so as to obtain the total phase difference formula +.>Taking the minimum value, recording the corresponding relation between C and r at the moment, wherein f is the focal length of the superlens and lambda 0 Is the midpoint of the wavelength range, r is the distance from the center point of the substructure to the center point of the superlens; the calculation process in step S2 uses a particle swarm algorithm.
S3, according to the result of the achromatic coefficient C obtained in the step S2, the achromatic coefficient C is combined with a film transmission phase formulaSetting the film material and the film thickness required for coating on the substrate so thatTaking the minimum value, will +.>As a new achromatic coefficient, the surface phase formula required for the substructure is obtained>Wherein n is the refractive index of the film material, d is the thickness of the film, k is an integer value which is introduced by considering the superlens manufacturing difficulty factor, and the value range is [0,3]；
S4, modeling and parameter scanning are carried out on the substructure, proper heights are selected, the corresponding relation between the radius of the substructure and the corresponding surface phase distribution is obtained, and the corresponding relation is recorded as a phase library;
and S4, the parameters scanned in the scanning process are the high and the radius of the substructure, and the calculation of the scanning process is realized by a time domain finite difference method.
S5, according to the surface phase formula obtained in the step S3, the due surface phase data of each substructure is calculated, then the radius value corresponding to the surface phase data is searched in the phase library obtained in the step S4, so that the radius of the substructure at each position is determined, and further each substructure is modeled according to the radius of the substructure at each position, the high-film material and the thickness obtained in the previous step, and further modeling of the complete superlens is realized, and the focusing performance and the achromatic effect of the superlens are calculated and simulated.
The theoretical basis of the design method is set forth below:
the present invention aims to provide a part of the phase compensation required for achromatism by the film layer by using the principle of transmission phase regulation.
In superlenses based on PB phase modulation, one widely used achromatic approach is,calculating the sum of the total phase differences due to phase changes caused by wavelength changes over a specified band, introducing a constant that minimizes the number of this sum, i.e.Minimum, wherein: />Is an ideal phase formula for a planar focusing superlens,φfor the designed superlens surface phase distribution, it should be a function related to r onlyThe method comprises the steps of carrying out a first treatment on the surface of the Where C is a constant introduced for the achromatic function or a function related to r only, we call the achromatic coefficient, the achromatic function can be achieved by calculating the appropriate C value to minimize the sum of the total phase differences. We record the achromatic constant obtained in the above procedure as C 1 。
In the achromatic method, due to the introduction of C, at any wavelength, the actual phase distribution always has a difference value from the ideal phase distribution, the difference value is determined by the wavelength difference, the position and the focal length, and the difference value is also provided by the unit structure, so that the deflection of light is influenced, the focusing effect of the superlens is weakened, and the achromatic range of the superlens is further limited.
Returning to the determination of the C value, if a base film layer of thickness d and refractive index n is added under the cell substructure. The different light rays will generate a phase difference when transmitted in the film material, and then the actual phase distribution formula will becomeOn the premise of general materials, nd is a constant or a variable with smaller fluctuation along with the change of wavelength, which can enable the substrate to provide a certain phase difference, and further enable the value of C to change integrally. Therefore, by designing a proper substrate thickness d, we can realize the control of C, increasing the flexibility of structural design.
It should be noted that d, which is required for regulating C, is very small, so that the regulation is actuallyIn the control process, the value of nd is added with proper quantity of lambda under the premise of target value 0 So that the thickness of the film layer reaches the range suitable for manufacturing, an integer k is introduced in the formula of step S3 in embodiment 1, the default value of k is zero, when the thickness d of the film layer is calculated to be smaller according to step S3 and the actual manufacturing difficulty is larger, the thickness d of the film layer can be properly increased by adjusting the value of k, and it should be noted that the value of k should not exceed 3 in consideration of that the excessively thick film layer causes group delay dispersion, and thus the suitable value range of k is [0,3]。
Therefore, in the modified design concept, the wavefront phase distribution corresponding to the unit substructure after the film is added will becomeWherein->The achromatic coefficient T after manipulation is provided by the cell substructure, unlike the achromatic data obtained by the original method. On the premise that d is smaller, the transmission phase difference does not deflect light, so when nd is reasonably set, compared with the prior method, the method can provide phase compensation for both the film layer and the substructures, and realize the effect of reducing the deflection degree of light with different wavelengths, so that the method can reduce the influence of achromatic coefficients on the focusing effect and the influence of wavelength change on the focusing effect while realizing the achromatic function, thereby realizing the improvement of the focusing performance of the achromatic superlens.
Furthermore, the achromatic coefficient C can be provided by designing film layers at different positions to have different thicknesses, so that the focusing effect is optimal, and considering the problem of actual processing difficulty, the concept is that the current cost is too high and the difficulty is too high, so that a flat film layer with a fixed thickness is still selected in the design method of the invention. On the basis, the superlens designed by the method is relatively easy to manufacture.
Furthermore, the design method of the invention is to implement achromatic coefficient regulation and control by the thought of strengthening the focusing effect at the central wavelength, and is basically applicable to all achromatic scenes.
Further, referring to fig. 1, the infrared short wave band achromatic superlens obtained by the design method of the present invention has a lens radius of 20um, a focal length of 90um, and a numerical aperture of 0.217. The super lens consists of a substrate and unit substructures which are arranged on the substrate according to a rule, wherein the substructures are made of SiO (silicon dioxide) 2 On which Si with a thickness of 0.101um is plated 3 N 4 The film and the substrates of the substructure are mutually combined to form the substrate of the integral superlens, the period of the substructure is 0.45um, the main body is a cylindrical micro-nano structure, the column material is silicon, the height of the column is 1um, and the radius is determined by the space position and the phase distribution. The focus offset of the integral lens caused by chromatic aberration on the infrared short wave band of 1.3um-1.7um is not more than 2%, the focusing efficiency is above 0.75, and the manufacturing difficulty is basically equivalent to that of a common superlens.
In addition, the radius of each unit substructure of the lens is different, but is between 0.05um and 0.2 um. The array of sub-unit structures is circularly arranged, and the number of the sub-structures on one radius is 67.
Fig. 2 is a partial image of a focal position of a common superlens according to a change of a wavelength of light, and seven light spots sequentially represent focusing effects of the superlens when the wavelength of incident light is 1.4um, 1.425um, 1.45um, 1.5um, 1.55um, 1.575um, and 1.6 um. When the wavelength is 1.5um, the focal position is 90um.
The seven light spots in fig. 3 represent the focusing effect of the superlens when the incident wave wavelength is 1.3um, 1.35um, 1.4um, 1.5um, 1.6um, 1.65um, 1.7 um. The focus is at 90um.
Comparing fig. 2 and 3, it can be seen that the superlens has good achromatic power over the infrared short wave band of 1.3um-1.7 um. The focus position thereof is not shifted by more than 2%.
Further, the improvement of focusing efficiency brought by the design method can be intuitively seen from fig. 4, which enables the super lens to still have focusing efficiency exceeding 0.75 when the incident wavelength is 1.3um, so as to meet the actual use requirement, while when the achromatic method of the existing method is used, the focusing efficiency is only 0.68 at the wavelength of 1.3um, and the design method is not suitable for the actual use scene, so that the design method widens the actual achromatic wavelength range of the super lens.
It should be noted that, in the actual design process, a step S6 should be added to the design method:
and S6, when the lens performance obtained by simulation cannot meet the requirement, returning to the step S1, resetting structural parameters of the unit substructure, including resetting the period, the film thickness, the material and the like, or returning to the step S3, and expanding the parameter scanning range.
It should be noted that in the description of the present specification, the descriptions of the terms "one embodiment," "example," "specific example," and the like mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Those of ordinary skill in the art will recognize that the embodiments described herein are for the purpose of aiding the reader in understanding the principles of the present invention and should be understood that the scope of the invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific modifications and combinations from the teachings of the present disclosure without departing from the spirit thereof, and such modifications and combinations remain within the scope of the present disclosure.
Claims (7)
1. A method for designing an achromatic superlens in an infrared short wave band, comprising the steps of:
s1, determining a target achromatic wave band according to requirementsThe super lens radius R, the arrangement cycle number of the substructures forming the super lens and the cycle T of the substructures are determined, the center point of the substructures is positioned at a distance from the lens center mT, and the arrangement cycle number and the cycle T of the substructures are determinedM is a natural number, the value range is [0, R/T ], and the substructure is a cylindrical nano rod made of silicon and taking glass as a substrate;
s2, according to a surface phase distribution formulaPhase difference sum formula corresponding to each substructurePerforming comprehensive calculation to calculate the value of achromatic coefficient C corresponding to each substructure at each position so as to obtain the total phase difference formula +.>Taking the minimum value, recording the corresponding relation between C and r at the moment, wherein f is the focal length of the superlens and lambda 0 Is the midpoint of the wavelength range, r is the distance from the center point of the substructure to the center point of the superlens;
s3, according to the result of the achromatic coefficient C obtained in the step S2, the achromatic coefficient C is matched with a film transmission phase formulaSetting the film material and film thickness required for coating film on the substrate to make +.>Take the minimum value, willAs a new achromatism coefficient, and further obtain a surface phase formula required to be provided by the substructureWherein n is the refractive index of the film material, d is the thickness of the film, k is an integer value which is introduced by considering the superlens manufacturing difficulty factor, and the value range is [0,3]；
S4, modeling and parameter scanning are carried out on the substructure, proper heights are selected, the corresponding relation between the radius of the substructure and the corresponding surface phase distribution is obtained, and the corresponding relation is recorded in a phase library;
s5, calculating due surface phase data of each substructure according to the surface phase formula obtained in the step S3, and searching a radius value corresponding to the surface phase data in a phase library obtained in the step S4, so that the radius of each substructure at each position is determined, and modeling is carried out on each substructure according to the radius of each substructure at each position to obtain the modeling of the complete superlens.
2. The method of designing an achromatic superlens according to claim 1, wherein said calculating in step S2 uses a particle swarm algorithm.
3. The method of claim 1, wherein the parameters scanned in the scanning process in step S4 are the high and radius of the substructure, and the calculation of the scanning process is performed by a finite difference method in the time domain.
4. The method of designing an infrared short wave band achromatic superlens according to claim 1, further comprising the steps of:
s6, when the lens performance obtained through simulation cannot meet the requirements, returning to the step S1, resetting structural parameters of the unit substructure, including resetting the period, the film thickness and the materials, or returning to the step S3, and expanding the parameter scanning range.
5. The method for designing an infrared short-wave band achromatic super lens according to claim 1, wherein the infrared short-wave band achromatic super lens has a radius of 20um, a focal length of 90um, and a numerical aperture of 0.217, and comprises a substrate and a unit substructure arranged thereon in a regular pattern, wherein the substrate material of the substructure is SiO 2 On which Si with a thickness of 0.101um is plated 3 N 4 The film, the substrates of the substructure are mutually combined to form the substrate of the integral superlens, the period of the substructure is 0.3um, and the main body is roundThe cylindrical micro-nano structure is characterized in that the cylindrical material is silicon, the height of the cylindrical material is 1um, the radius is determined by the spatial position and the phase distribution, the focus offset of the integral lens on an infrared short wave band of 1.3um-1.7um caused by chromatic aberration is not more than 2%, and the focusing efficiency is above 0.75.
6. The infrared short wave band achromatic superlens of claim 7, wherein the radii of each cell substructure are different, but each is between 0.05um and 0.2 um.
7. The infrared short wave band achromatic superlens of claim 7, wherein the array of sub-unit structures is circularly arranged, and the number of sub-structures on a radius is 67.
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